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The kinematics of a particle with the upper bound on the particle's speed (amodification of classical kinematics where such a restriction is absent) hasbeen developed in [arXiv:1204.5740]. It was based solely on classical mechanicswithout employing any concepts , associated with the time dilatation or/andlength contraction. It yielded the 1-D Lorentz transformation (LT), free ofinconsistencies (inherent in the canonical derivation and interpretations ofthe LT). Here we apply the same approach to derive the LT for the 3-dimensionalmotion of a particle and the attendant law of velocity composition. As aresult, the infinite set of four-parameter transformations is obtained. Therequirement of linearity of these transformations selects out of this set thetwo-parameter subset . The values of the remaining two parameters ,dictated byphysics of the motion, is explicitly determined , yielding the canonical formof the 3-dimensional LT. The generalized law of velocity composition and theattendant invariant ( not postulated apriori) of the motion are derived, As inthe one-dimensional case, present derivation, as a whole, does not have anyneed in introducing the concepts of the time dilatation and length contraction,and is based on the classical concepts of time and space.

Special relativity as classical kinematics of a particle with the upper  bound on its speed. Part II. The general Lorentz transforrmation and the  generalized velocity composition theorem